A fast Chebyshev's method for quadratic equations. (Q1417017)

In order to solve a quadratic equation \(F^{\prime \prime }(x)=B\), where \(B\) is a bilinear constant form, third-order methods are considered. To this end, the authors use multiresolution representation of data, standard forms of a matrix and of a bilinear operator and propose an adaptive Chebyshev method, whose convergence is proved (Theorem 1). Numerical examples are also presented.